AI-enabled manufacturing process discovery

Abstract

Discovering manufacturing processes has been largely experienced-based. We propose a shift to a systematic approach driven by dependencies between energy inputs and performance outputs. Uncovering these dependencies across diverse process classes requires a universal language that characterizes process inputs and performances. Traditional manufacturing languages, with their individualized syntax and terminology, hinder the characterization across varying length scales and energy inputs. To enable the evaluation of process dependencies, we propose a broad manufacturing language that facilitates the characterization of diverse process classes, which include energy inputs, tool-material interactions, material compatibility, and performance outputs. We analyze the relationships between these characteristics by constructing a dataset of over 50 process classes, which we use to train a variational autoencoder (VAE) model. This generative model encodes our dataset into a 2D latent space, where we can explore, select, and generate processes based on desired performances and retrieve the corresponding process characteristics. After verifying the dependencies derived from the VAE model match with existing knowledge on manufacturing processes, we demonstrate the usefulness of using the model to discover new potential manufacturing processes through three illustrative cases.

Introduction

Manufacturing is a cornerstone of human societal development, propelling advancements that have fundamentally improved our way of life. In the beginning, the Stone Age introduced rudimentary tooling, establishing the link between human culture and technological progress (1). Subsequently, the Bronze Age and Iron Age arrived and innovated these tools through the invention of the smelting process, enabling the manufacturing of strong and durable bronze and iron tools for farming in challenging terrains (2). This interwoven relationship between manufacturing process innovation and economic development expanded during the Industrial Revolution. Today, complex manufacturing processes continue to drive our society and culture while providing societal benefits. Examples include metal 3D printing for customized orthopedic implants (3), nanolithography for submicron transistors in electronic devices (4), and incremental sheet metal forming, which reduces the cost of producing small quantities of highly customized lightweight parts for the automobile and aerospace industries (5).

Conceptualizing new processes requires anticipating new constraints, such as manufacturing in space, a natural extension of our reach and desire as explorers. To accelerate process innovation, an accessible tool or platform designed to address constraints like energy usage, process time, and dimensional tolerances is needed. We propose a methodology for generating candidates for future manufacturing processes, grounded in the interaction between tool and workpiece, the fundamental ingredient in manufacturing. This interaction, driven by energy inputs and material state changes, ultimately determines critical characteristics such as dimensional tolerance and surface quality. Our goal is to develop a platform where users can input desired process characteristics, such as input energy type, and receive the performance of the potential manufacturing process as output. This capability facilitates early-stage process ideas and innovation, enabling exploration of nonexisting manufacturing possibilities—like magnetically controlled additive manufacturing—by allowing users to conceptualize new process pathways and optimize characteristics according to unique needs and constraints.

We initiate this process generation platform by developing a unified manufacturing language for characterizing a diverse range of processes, for example, bringing biomachining and injection molding into a single domain. To conceptualize our manufacturing language, we first review existing process ontologies and selection procedures used in determining a manufacturing process to differentiate our approach in process discovery.

Ontologies and selection of manufacturing processes

The absence of a systematic procedure for synthesizing manufacturing processes stems from the highly context-specific nature of manufacturing language. Traditionally, each manufacturing process has its own language that encapsulates all possible processing parameters and operations under one or many glossaries, leading to shared keywords with different meanings (6). For example, the word “resource” can signify various meanings based on the context. In the context of process management, “resource” can signify the quantity of material or feed stock fueling the manufacturing process. While in process planning, “resource” refers to a machine’s list of capabilities. Currently, there is no universal language that bridges the gap between processes across different scales, from micro- to macroscopic, and diverse energy inputs, such as mechanical to chemical.

Efforts to unify manufacturing language began due to semantic differences, motivating researchers to develop process-oriented ontologies. These ontologies use neutral vocabulary to prevent misinterpretations, allowing the exchange of process and product descriptions across a hierarchy of classes representing various manufacturing areas, such as production, planning, and resources (7, 8). Depending on the application, manufacturing ontologies can be used to model cost estimation (9), define process capabilities (10), and manage manufacturing resources (11).

An example of resource management is demonstrated in the Capability Model outlined in the manufacturing resource management ontology (MaRCO) (11). This model starts with the capability’s natural name, such as “Milling” and “Drilling” classified under categories like “material removal,” and describes it as a “resource” using parameters like “Moving,” characterized by “speed” and “acceleration.” While this ontology provides a common understanding among different process resources, it requires processes to share similar capabilities for effective matchmaking based on product requirements. Therefore, process ontologies focus on select domains. For instance, MaRCO focuses on mechanical processes involving material transport, removal, and deformation. This limitation is common in other process ontologies, such as the Additive Manufacturing Ontology (AMO) (12), Computer Aided for Manufacturing Process Selection (CAMPS) for forging and casting (13), and the Basic Formal Ontology (BFO) for CNC machining (14). Generally, manufacturing ontologies are built upon existing ontology frameworks, most commonly the Web Ontology Language (OWL) (15). While OWL provides interoperability and streamlined information management, significant time and resources are required to extend process modeling beyond a specific process domain using the OWL.

On the other hand, manufacturing process selection procedures provide a numerical approach for identifying the optimal process based on criteria such as cost requirements (16) and multiple factors like part quality and manufacturing time (17). These procedures establish a ranking system driven by the capability limits of the included processes. These limits, derived from process limitations detailed in textbooks, include features such as achievable tolerances, surface finishes, and production rates (18). To incorporate geometric information, a process’s ability to manufacture complex parts is categorized as “Low,” “Medium,” or “High,” and cost is categorized in similar way (17). Based on the user’s desired set of capabilities, these limits are used to curate the ranking system, illustrating the optimal process given the specified criteria.

In practice, identifying the best process for a task can be quickly performed on-site by manufacturing experts without automated systems. This short-term solution has resulted in limited progress on universal process selection and process discovery over several decades. Emerging needs for increasing part complexity and performance necessitate rapid process discovery beyond the scope of an individual’s manufacturing knowledge and experience. To initiate systematic exploration and discovery of new manufacturing processes, exploring generative models from machine learning provides an avenue for designing and generating new processes based on future constraints rather than selecting existing processes that meet current constraints using a recommendation system. To initiate process discovery, we first build the training data by developing a manufacturing language designed on the principles of neutral language—incorporating critical characteristics commonly seen in process selection procedures while extending beyond the limitations of process-specific ontologies.

Manufacturing process language

Based on the fundamental understanding of how manufacturing processes work, we conceptualize the data structure with four essential categories as illustrated in Fig. 1, to describe an arbitrary manufacturing process. Each category encompasses characteristics that detail the process’s energy inputs, workable materials, tool–workpiece interaction, and performance outputs. A total of 21 characteristics are used to describe a manufacturing process. The framework is flexible to include additional details, such as expected part strength, to further refine the process description.

Energy inputs

The manufacturing language starts by characterizing a process’s energy inputs using the selection marked in blue (first branch) in Fig. 1. The energy sources (e.g. mechanical, conduction, convection, electrical, chemical, magnetic, and radiation) are commonly used for initiating interactions between the tool and workpiece. These interactions alter the material’s properties, geometry, and surface texture. For example, mechanical energy is utilized in operations such as milling and incremental forming. In milling, the mechanical energy from a rotating drill bit removes material, whereas in incremental forming, material is deformed by mechanically pressing the tooling against the workpiece.

We categorize thermal energy into three distinct modes of heat transfer: conduction, convection, and radiation. For example, processes like fused deposition modeling, driven by resistive heating, rely primarily on conduction with minor contributions from convection and radiation. In contrast, processes such as selective laser sintering, which utilizes a laser beam, are predominantly driven by radiation, with moderate contributions from conduction and convection.

Although most mechanical energy in manufacturing is realized through electrical motors, our language definition focuses on the most direct form of energy at the tool–workpiece interface. For electrical energy, we consider energy transmitted directly to the tool or workpiece, such as in electrically assisted incremental forming (19), electron beam machining (20), and robotic arc welding (21). Similarly, chemical energy involves inducing chemical reactions to alter the workpiece. An example of combining electrical and chemical energy is electrochemical machining, where an electrical current is passed through the tooling to dissolve a metal workpiece, and electrolysis removes the metal hydroxide. Lastly, magnetic energy is utilized to induce controlled behaviors via a magnetic field, as seen in managing tooling oscillation in ultrasonic machining and focusing the beam in electron-beam machining.

To measure and distinguish the driving energy input and contributing energy sources transmitted through the tool, workpiece, or both, we assess the applied energy on a scale from 0 to 5. The categories are absent (0), low (1), medium (2), high (3), very high (4), and extreme (5). This methodology evaluates the energy magnitude based on the process’s input energy relative to the workpiece volume.

Material compatibility

The next category in Fig. 1, the second branch and colored in pink, describes the compatibility of the workpiece material with the process. Material selection spans metals, polymers, wood, ceramics, and glass. For each process, material compatibility is indicated as either incompatible (0) or compatible (1). The current framework focuses on describing the compatibility of materials at a fundamental level, representing whether a process can utilize a given material type, without specifying detailed characteristics such as material ratios in a composite system. This approach reflects the generality and flexibility inherent in many manufacturing processes, where material ratios are often determined by user requirements or application needs.

Tool–workpiece interactions

To capture the tool–workpiece interaction of a process, shown in yellow (the third branch) in Fig. 1, we describe the feature size produced during a single toolpath. This interaction represents a fundamental working principle shared across manufacturing process (22). The tool–workpiece interaction emphasizes that minimal feature sizes are closely tied to machine resolution, which is a key performance metric across many manufacturing processes. We represent this performance metric by defining several aspects of the tool–workpiece interaction: volume change, affected volume per tool–workpiece interaction, tool and equipment cost, and specialized tooling.

Volume change indicates whether material is removed (0, part volume decreased), transformed (1, part volume stayed constant), or added (2, part volume increased). The affected volume, ranging from $10−3mm3$ to $0.1m3$⁠, specifies the minimal volume of material locally impacted by a single toolpath, this characteristic is independent of the actual workpiece volume. Tool and equipment costs range from low (1) to very high (4), with tool-less manufacturing processes, such as selective laser sintering, assigned with no tooling cost (0). Additionally, we note whether specialized tooling is required for the process, which includes tools such as mold cavities needed to complete the manufacturing process.

Outputs

What a manufacturing process can do is essential in describing a process. We define the output types, highlighted in green (the fourth branch) in Fig. 1, which are crucial for process selection. We define process time as the duration required to complete a part, ranging from subseconds (e.g. a stamping operation) to an entire day (e.g. fine polishing or 3D printing). The level of geometric complexity achievable by a process is categorized from low (1) to very high (4). Surface quality is defined by the roughness average, ranging from 1 nm to 10 mm, achievable by the process. Lastly, we utilize the International Tolerance Grading (IT Grade) to define a process’s range of dimensional tolerances, where higher IT Grade values indicate looser tolerances (23).

Each manufacturing process within our dataset of 55 unique process classes is represented by the 21 process characteristics shown in Fig. 1. Table 1 provides examples of how our manufacturing language describes manufacturing processes. The values assigned to each process serve as a reference for characteristics and may vary slightly depending on machine’s capabilities. To extend the language’s versatility for process discovery beyond our static dataset, we utilize deep learning to model the dataset’s distribution using a generative model, enabling users to explore and interpret new process ideas.

AI-enabled discovery

Generative modeling (24), a versatile deep learning approach, has shown significant potential in learning the distribution of input datasets to synthesize new data points that were not originally present. This capability has driven rapid advancements across various fields, including the generation of new high-entropy alloys in material science (25), the identification of photoacid generator candidates for drug discovery (26), and the development of pathways for inverse molecular design (27). Common generative frameworks include recurrent neural networks (RNNs) (28), generative adversarial networks (GANs) (29), and variational autoencoders (VAEs) (30). Recently, there has been a shift towards natural language processing (NLP), inspired by widely recognized models like GPT-4 (31). In parallel, realistic image and video generation has advanced through diffusion models like SORA (32, 33). Despite this shift, key concepts from earlier generative frameworks remain effective, particularly the probabilistic interpretation of latent space in VAEs.

Once a generative model learns the distribution of the input data, the latent space provides an exploratory environment where unpopulated regions can be sampled and analyzed (34, 35). In this work, we hypothesize that the latent space can serve as a platform for analyzing the distribution of our manufacturing dataset for designing processes based on desired process outputs or constraints. To test this hypothesis, we follow the proposed approach shown in Fig. 2. This approach begins with (i) developing a VAE model to learn the distribution of our manufacturing dataset, followed by (ii) latent space visualization, and (iii) exploration of each characteristic and its dependencies in latent space for curating process design. In the following section, we review the theory behind the VAE architecture to highlight its advantages in generating new data points for manufacturing process discovery.

Variational autoencoders

VAEs provide a probabilistic model built using an encoder–decoder architecture, with a key distinction from traditional autoencoders (AEs). While AEs encode the input data into a lower-dimensional latent space using a deterministic approach, VAEs are designed with a generative objective. Specifically, AEs focus on reconstructing the input data, which limits their ability to generate new data points. In contrast, VAEs aim to maximize the Evidence Lower Bound (ELBO, denoted as $L(θ;x(i))$⁠), which represents the marginal-likelihood estimation (⁠$logp(x(i))$⁠) of the input data (⁠$x(i)$⁠). By maximizing the ELBO, VAEs yield a probabilistic interpretation of the latent space (⁠$z(i,l)$⁠), which is defined by the number of elements (i) and the number of samples (l). The loss function used in this study, based on Kingma and Welling’s formulation (36), is expressed as:

where VAE introduces an additional loss term over AE known as the Kullback–Leibler (KL) divergence (36). By minimizing the KL divergence, the model maximizes the marginal-likelihood estimation using the learned parameters (θ) of the model. The KL divergence term is analytically formulated by mapping the mean $μ(x)$ and variance $σ(x)$ vectors of the input data to a standard normal distribution $N(0,1)$⁠. Minimizing the KL loss (⁠$LKL$⁠) also serves as a regularizer, ensuring that the encoded inputs are mapped into this normal distribution. Prior work on VAEs has shown that the hyperparameter β  $∈[0,1]$ in Eq. 1 can be adjusted to control the strength of the regularization term (37). Without regularization (⁠$β=0$⁠), the traditional AE is recovered and governed solely by the reconstruction loss (⁠$LRecon$⁠). This reconstruction loss, often measured using mean square error (MSE), quantifies the difference between the original input and the VAE’s predictions.

The predictions provided by VAEs, which assume a normal distribution of the input data, enable sampling within the latent space using the equation $z(i)=μ(i)+σ(i)⊙ϵ(l)$⁠, where $ϵ(l)∼N(0,I)$⁠. This sampling process, known as the re-parameterization trick, decouples the stochasticity from the latent variables and allows the model to remain differentiable, which also stabilizes the training process. Additionally, by re-parameterizing, VAEs ensure that the gradients of the sampling process can be propagated through the network during training, facilitating optimization using gradient-based algorithms. Although VAEs approximate the input data as normally distributed, this assumption does not introduce significant error and is considered an effective approach for back-propagating error during the sampling process (38).

VAE applications in manufacturing process discovery

The theory behind VAEs has facilitated their broad application in manufacturing, including generating realistic images of defects on metal surfaces for defect classification (39), establishing multivariate process monitoring of thin-film-transistor liquid-crystal display processes (40), and predicting geometric dimensions and tolerance of machined workpieces by visualizing dataset clustering in 2D latent space (41). However, using the latent space for inverse prediction in manufacturing process design, starting with the desired properties and working backward to identify the necessary components or operations, has been limited. To explore the relationship between the characteristics in our manufacturing dataset, we develop a VAE model to uncover dependencies among energy inputs, material compatibility, tool–workpiece interaction, and outputs.

Results

Manufacturing process platform

Once the VAE model is developed, the encoder visualizes the distribution of our manufacturing process dataset in the latent space, as illustrated in Fig. 3. A balanced distribution of the reconstruction and KL loss result in a central clustering of input data around the origin of the 2D latent space (N(0,1)). At this origin, processes are categorized by their mode of material interaction (removal, transformation, or addition). Figure 3B shows the clustering of traditional removal and transformative processes, while Fig. 3D highlights the grouping of nontraditional processes. Particularly, laser-induced plasma micro-machining (LIPMM) and electron beam machining appear in Fig. 3D, emphasizing their deviation from the standard mechanical-driven processes observed in Fig. 3B. This latent space distribution of processes provides a platform for process selection and generation, as demonstrated by the user-selected points marked by the orange “x” in Fig. 3. These points are decoded using their latent coordinates to generate the corresponding process characteristics, as presented in Table 2.

Instead of manually inputting coordinates into the decoder for desired characteristics, we can input all coordinates within a specific area of the latent space. This approach produces a feature map that visualizes the distribution of each characteristic across the latent space. Figure 4 showcases the distribution of the energy requirements (Fig. 4A–G) within the latent space, along with the distribution of addition, transformative, and removal-based processes (Fig. 4H).

The visualization of feature maps extends beyond observation to analyzing the dependencies between process characteristics. To explore these dependencies, we demonstrate a use-case based on future manufacturing constraints, particularly for in-space manufacturing. In a vacuum environment, heat transfer through conduction and convection is not possible. Given these limitations, we can realize an inverse search strategy to conceptualize processes that do not utilize conduction and convection for material removal, transformation, and addition. By guiding our process generation based on volume changes, we focus on specific characteristics: process time for material removal to indicate removal speeds, dimensional tolerances for material forming to assess geometric accuracy, and affected workpiece volume for material addition to evaluate process scalability.

The feature maps shown in Fig. 5 are generated by excluding the conduction and convection regions. Specifically, the zero-value regions from Fig. 5B (i.e. no conduction) and D (i.e. no convection) are overlaid and marked as valid regions for process discovery, while all other regions are excluded for consideration. These maps are then further refined by categorizing them according to volume changes using Fig. 4H—removal, transformation (None), and addition—resulting in three distinct feature maps. The final feature maps, presented in Fig. 5A–C, overlay the respective process characteristic of interest (e.g. dimensional tolerance, as shown in Fig. 2) onto the valid region: A) process time for material removal, B) tolerances (IT Grade) for material transformation, and C) affected volume for material addition.

For each case, we search and generate processes using an automatic selection criteria based on the valid region of process discovery. Processes ending with “1” are generated using the maximum value achievable for the process characteristics of interest (process time (A), tolerance (B), affected volume (C)). Processes ending with “2” pertain to the minimum value achievable per respective characteristics of interest. “3” searches for the median value. Lastly, “4” is picked manually in areas far from the origin cluster of processes.

Case 1: removal speeds in subtractive processes

Material removal processes such as machining are designed to offer rapid material removal speeds, high surface quality, and cost-effectiveness (42). Traditional machining operations, driven by mechanical energy, are suitable for in-space manufacturing due to their energy requirements. In Fig. 5A, various regions in the latent space highlight potential process candidates based on the absence of conduction and convection. Near the origin, traditional machining operations cluster (A2 and A4), while nontraditional processes utilizing chemical (A1) and radiation energy (A3) are positioned further away. The resulting process characteristics are detailed in Table 3.

Process A1, shown in Fig. 5A, demonstrates the slowest removal rate, with a process time of (⁠$104s$⁠), positioning it near processes like chemical machining and biomachining that offer slow but precise material removal at the micrometer level. The slow process time of A1 is due to its high (3) reliance on chemical energy, which characterizes A1 as a variation of chemical machining. This process involves submerging the workpiece in a chemical bath (etchant) that dissolves unprotected areas, while a maskant shields the regions meant to remain intact. Process A1, using this method, removes $10mm3$ of material per tool–workpiece interaction, produces a smooth surface finish (⁠$1μm$⁠), and achieves tight tolerances (IT Grade 6). The key difference between chemical machining and A1 is the increased affected volume (1 to $10mm3$⁠) and the material compatibility with ceramic and glass workpieces instead of metals.

In contrast, process A2 achieves the fastest (1 s) material removal rate by utilizing a low (1) amount of mechanical energy to remove small volumes (⁠$1mm3$⁠) from metal and wood workpieces. These characteristics provide insight that A2 employs a high-speed drill bit, commonly used as a finishing operation on light metals and wood workpieces, with a milling machine to penetrate and remove material. The neighboring processes, such as include route machining and reaming, contributes to A2’s characteristics: low (1) equipment/tool cost, smooth surface finish (⁠$1μm$⁠), and tight tolerances (IT Grade 8).

Process A3 explores nontraditional removal processes, using a beam-driven approach with a process time of 10 s. A3 utilizes extreme (5) levels of radiation, assisted by high (4) electrical and medium (2) magnetic energy. This process is a variation of electron beam machining, where a high-velocity electron beam is used to vaporize material. The beam’s control and focus are achieved through the use of a magnetic field. A3 removes $1mm3$ of material per tool–workpiece interaction, resulting in a rough surface finish (⁠$100μm$⁠) and tight tolerances (IT Grade 5).

Lastly, process A4, located within the central cluster but horizontally offset into an input data-void region, is a purely mechanical-driven process requiring extreme (>5) forces. A4 removes $100mm3$ of material per tool–workpiece interaction. With its broad material compatibility and extreme mechanical requirements, A4 represents a water/projectile jet-based process. This process propels a projectile—such as water, abrasive particles (sand), or both—at hundreds of meters per second through a nozzle. The nozzle’s orifice focuses the projectile into a beam capable of cutting through a wide variety materials. The high energy requirements result in very high (4) tooling and equipment costs, similar to those of electron beam machining. Despite A4’s high removal rate, its loose tolerances (IT Grade 12) and rough surface finish (⁠$10μm$⁠) makes A4 less viable compared with other removal-based processes.

Case 2: tolerances in transformative processes

A key objective in transformative processes is to achieve high geometric accuracy and complexity. In the latent space shown in Fig. 5B, transformative processes cluster based on their energy inputs, with a clear distinction between processes using conduction or convection and those using alternative energies. The valid region, marked by the absence of conduction and convection, include processes driven by mechanical, chemical, electrical, and radiation energy. In contrast, the lower region (transformative processes below B3) include processes such as die casting, shell molding, and hot rolling, which rely on conduction and convection. The process characteristics for transformative processes are detailed in Table 4.

Process B1, characterized by loose tolerances (IT Grade 12) and a high (3) amount of mechanical energy, represents processes such as hemming and stamping. These sheet metal forming techniques are known for their ability to rapidly shape large volumes of material using tooling that involves a punch and a die. B1 establishes the tolerance limit for transformative processes that do not use conduction and convection.

In contrast, process B2 achieves the tightest tolerances (IT Grade 6) with a low (1) amount of mechanical energy combined with a high (3) amount of chemical energy. B2 results in long process times (1,000 s), smooth surface finishes (⁠$1μm$⁠), and affects up to $100mm3$ of polymer workpieces. Due to the limited material compatibility, the need for specialized tooling, and reliance on a high chemical reaction, B2 realizes the reaction injection molding process. This process involves reactive liquid polymers mixed within a low-pressure mold to transform and solidify the material workpiece.

Process B3 represents a low-energy consumption method with a low (1) radiation energy input, located between processes such as reaming, laser polishing, and Continuous Liquid Interface Production (CLIP). B3 offers broad material compatibility, including metals, polymers, ceramics, and glass. Although similar to laser shock peening, which employs high pressures (1 GPa–1 TPa) and energies exceeding 1 GW to induce residual stresses in a workpiece, process B3 does not meet the intense energy requirements of laser shock peening. Instead, it offers a low-energy alternative for material forming, providing insight into a reduced energy-intensive option for achieving precise tolerances and broad material compatibility.

Process B4 is a purely chemical-based transformative process that employs a medium (2) amount of chemical energy. This process utilizes an acid solution, such as hydrochloric acid, to chemically alter the surface of metal workpieces. An example is acid pickling, which removes soluble iron oxides from the metal surface without dissolving any base material (43). Unlike traditional acid pickling methods that incorporate thermal inputs to accelerate the reaction, B4 relies solely on chemical reactions, resulting in a process time on the order of days.

Case 3: volume print size in additive processes

Additive processes are crucial for rapid prototyping and manufacturing highly complex geometries. In large-scale industrial applications like turbine blade production, substantial volumes of layer-by-layer deposition are required. The high material efficiency of 3D printing, compared to subtractive methods, make additive a promising option for in-space manufacturing, where feedstock can be directly converted into intricate workpieces in orbit on an as-needed basis. However, a significant challenge in a vacuum environment is the absence of conduction and convection heat transfer, which can adversely affect the melted deposited material or melt pool and layer adhesion quality. Considering these limitations Fig. 5C reveals regions the behavior of affected volume for material addition processes when independent of conduction and convection. The resulting process characteristics are detailed in Table 5.

Process C1 is designed for producing the largest volume prints, utilizing a high (3) amount of mechanical energy to achieve significant material deposition. This method represents a cold working variation of sheet lamination, beginning with an initial layer of sheet metal on a build platform. Subsequent layers are added using a roller, which compresses each layer into the previous one to ensure bonding, achieved through adhesion. This process is suitable for metals and polymers, especially viscoelastic polymers, as reflected in C1’s material compatibility. Due to the extensive affected volume (⁠$0.01m3$⁠), process C1 results in loose tolerances (IT Grade 13) and a rough surface finish (⁠$100μm$⁠).

In contrast, process C2 achieves the smallest printing volume, producing a minimal volume of $10−3mm3$⁠. This process uses a very high (4) amount of radiation and low (1) amount of chemical energy, with a process time of 1,000 s. C2 is compatible only with polymers, suggesting it relies on radiation-induced polymerization for material addition. This method aligns with processes such as CLIP and stereolithography. These techniques begin with a bath of liquid resin, with an oxygen-permeable window at the bottom allowing UV light to pass through. Controlled exposure to UV light solidifies desired regions of the resin. A build plate at the top moves the solidified regions away from the window, enabling fresh liquid resin to flow into place for the next layer. This method is known for achieving tight tolerances (IT Grade 7) and smooth surface finishes (⁠$1μm$⁠), aligning closely with the characteristics of process C2.

Similar to process C2, process C3 shares similar characteristics but extends its material compatibility to include ceramics and glass workpiece material in additions to polymers. Due to the enhanced material capabilities, C3 utilizes powdered feedstock for the additive manufacturing of ceramic and glass workpieces (44, 45). Unlike C2, where the build plate is positioned at the top, C3 places the build plate at the bottom, with the laser source located above. During the process, the powdered feedstock is selectively solidified by the laser. After each layer is solidified, the build plate lowers to allow fresh powdered material to be deposited, enabling the next layer to be built.

Process C4, while sharing the same types of energy inputs and as C3 and C2, differ in energy usage. Process C4 employs a low (1) amount of radiation energy and a medium (2) amount of chemical energy. As a result, process C4 experiences longer process time (⁠$104$ s), looser tolerance (IT Grade 9), and reduced geometry complexity (low). This process highlights how lower energy inputs can impact the output characteristics. With insufficient energy, the process performance is reduced, offering a lower-radiation alternative to C2.

Validation of discovered processes

We validate the discovered manufacturing process ideas, shown in Tables 3–5, by focusing on the trends revealed in each use case and upper/lower bound of performance rather than validating the exact numerical values.

Subtractive processes

The trends in the first use case reveal a consistent tradeoff between tolerance precision and processing speed, as seen in the tighter tolerances achieved by nonmechanical processes (A1, A3) at the cost of higher process times and equipment expenses. Furthermore, processes supporting broader material compatibility, such as A4, tend to compromise on precision. These findings emphasize the balance required between process efficiency, material compatibility, and operational costs in subtractive manufacturing.

The upper bound of performance is demonstrated by A3, which combines multiple energy sources to achieve a process time of 10 s, capable of removing $1mm3$ of material per interaction, with tolerances reaching IT Grade 5. However, this comes with a very high tool/equipment cost (4). On the lower bound, A2 uses minimal mechanical energy, enabling rapid material removal (⁠$1mm3$⁠) at the lowest tool/equipment cost (1). While achieving smooth surface finishes (⁠$1μm$⁠), it remains limited to metal and wood workpieces.

Transformative processes

In the second use case, dimensional tolerances in transformative processes, we validate the discovered processes by identifying key trends. Processes driven purely by mechanical energy (B1), such as sheet metal bending, are fast (10 s) and capable of affecting large material volumes (⁠$10cm3$⁠) all at once. They also exhibit loose tolerances and rough surface finishes. These issues stem from springback effects in metals and tool wear. These characteristics represent the lower bound for dimensional tolerance. Conversely, transformative processes not dominated by mechanical energy, such as processes B2–B4, achieve significantly tighter tolerances and smoother surface finishes. However, this dimensional accuracy comes at the cost of increased process time and reduced affected volume. These processes represent the upper bound of dimensional accuracy. The trends demonstrated highlight that hybrid transformative processes (B2) that incorporate additional energy sources can overcome the limitations of mechanical-driven approaches to improve tolerances and surface finishes.

Additive processes

In the third use case, we validate the discovered processes by analyzing the relationship between printing volume, process time, dimensional tolerance, and energy criteria. Processes C2 and C3 demonstrate similar energy input types but at varying degrees, revealing that the most dimensionally accurate parts (IT Grade 7) are achieved using chemical and radiation energy for materials such as polymers, ceramics, and glass. However, this accuracy comes with a tradeoff: significantly smaller printing volumes (⁠$10−3cm3$⁠) and longer process times (1,000 s). These processes represent the lower bound for volume prints. Process C4 highlights the effect of a material change from polymer-based to metal-based workpieces. This transition results in an increase in process time from $103$ s to $104$ s, illustrating the greater complexity and energy requirements for additive manufacturing with metals. Conversely, Process C1 achieves the largest printing volume, but its reliance on mechanical processes for metal and polymer workpieces results in medium process times (⁠$102$ s), rougher surface quality (⁠$100μm$⁠), and looser dimensional tolerances. This process represents the upper bound for volume prints. These trends highlight the need to balance the amount of volume printed; otherwise, long process times (1,000 s) or loose dimensional dimensions (IT Grade 13) are realized.

Reconstruction accuracy

It is known that the reconstruction accuracy of deep learning models improves as a power-law with the increase in data utilized during training (46). This relationship explains why models trained on extensive datasets often report accuracies above 90%. However, accuracy alone is not the definitive metric for evaluating the reliability or effectiveness of generative models. For generative modeling the primary objective is to synthesize realistic data, therefore the true evaluation is in the quality, diversity, and application-specific soundness of the generated data.

Our in-house manufacturing dataset, while currently limited to 110 processes each with 21 process characteristics for (110, 21) data points, provides a diverse range of traditional and nontraditional removal, transformative, and additive processes. By employing proper hyperparameter tuning and regularization techniques, we ensure the generative model outputs a diverse range of synthesized process candidates, as seen in our use cases. The reconstruction accuracy achieved by our VAE model is approximately 74% across various random seeds, with each seed introducing a different set of probabilistic interpretations. This level of consistent accuracy highlights the interpretability of our dataset structure, as well as the effectiveness of our data augmentation and hyperparameter tuning strategies.

To maintain consistency with the integer format of the input data, the output is rounded to the nearest half after reconstruction, ensuring practical and interpretable results. The largest inaccuracies are observed in process characteristics with wide value ranges, such as IT Grade, which spans from 3 to 15 in our dataset. For IT Grade, the mean deviation is 2.0, with a standard deviation of 2.5, indicating variability in the reconstruction accuracy for this process characteristic.

Discussion

In this study, we introduce a manufacturing process language designed to describe multienergy processes across a range of length scales, unifying different process classes under a single framework. This language uses a numerical format to quantify process characteristics, such as energy inputs and dimensional tolerances. We develop a dataset of 55 unique manufacturing process classes built using this language to train a VAE model for analyzing the dependencies between these characteristics. The VAE’s latent space serves as a manufacturing platform for process selection and generation, facilitating early-stage exploration of process candidates prior to their real-world application.

This latent space validates the effectiveness of our language by demonstrating a strong alignment with established manufacturing knowledge through the generation of process candidates that closely resemble real-world processes. For instance, process A4 represents a large-scale water/projectile jet-based process, B2 corresponds to the reaction injection molding process, and C3 realizes sheet lamination. Most interestingly, these candidate processes were generated based on specific process constraint criteria. Our use cases investigate the effects of energy limitations, particularly in scenarios where conduction and convection heat transfer are absent, as relevant to space manufacturing. Through these use cases, we illustrate the diverse range of process capabilities under these conditions when considering whether the material is removed, transformed, or added.

Our results from Table 3 to 5 demonstrate that traditional machining operations, such as milling and drilling, achieve faster removal rates compared with nontraditional subtractive processes like biomachining and electrical discharge machining. Transformative processes can achieve tighter tolerances when assisted by energy sources alongside mechanical energy. Additionally, increasing printing volumes in additive processes results in longer manufacturing times and looser tolerances. This validation supports our manufacturing platform to inspire new ideas for innovative process design.

Our future work will focus on extending the material characterization framework from a single-level homogenized property to a multilevel hierarchical structure that incorporates material ratios. This extension will enhance the “Materials” category (Fig. 1) by including the specific ratios in which materials are combined, thus providing insight to the formation and characterization of composites.

With this generative manufacturing process platform, we can explore scenarios such as achieving the tightest tolerances, smoothest surface finishes, and fastest process times using minimal energy. Additionally, the model can identify the best performance at the lowest cost. This “what if” approach enables the exploration of novel combinations of process characteristics, addressing future manufacturing challenges.

In addition, we aim to leverage the manufacturing process platform as a planning tool to guide early process development towards eventual real-world application of new manufacturing processes. Specifically, we will be focusing on processes with unique energy synergies capable of achieving performances outcomes beyond current industry capabilities. This approach will allow us to evaluate the practical viability of our platform’s generated processes and refine the platform for improved industry application.

Lastly, to expand the output of the manufacturing platform, we aim to incorporate the 3D geometry of parts that can be manufactured by a given process. Integrating 3D geometry with process characteristics will enable us to correlate these characteristics with specific geometrical requirements. Achieving this combination of different input types will require the use of a multimodal VAE model, which can handle multiple modalities such as text, images, and 3D meshes for generative purposes (47). By employing this model, we can design for desired process characteristics and retrieve their corresponding part geometries, further enhancing our platform’s utility for manufacturing process design and discovery.

Material and methods

Building the manufacturing dataset

To build the manufacturing dataset, we conducted an extensive literature search spanning publications (48), online data sheets (49, 50), and interviews with manufacturing experts. Given the scarcity of information regarding process characteristics, we ensure consistency and accuracy by comparing similar processes when adding new entries to the dataset. For instance, milling should have higher values for process time, affected volume, and IT Grade range (indicating looser tolerances) compared with micro-machining. While the dataset values may vary slightly in practice, small adjustments to these reference values do not significantly impact the conclusions drawn from the results.

We maintain the underlying structure of the manufacturing dataset during encoding by utilizing L2 normalization (⁠$‖x‖2$⁠) to normalize our dataset (x) using Eq. 4. Here, n is the total number of components in the vector (process characteristics), and $xk$ represents the kth component of x. The ratio between the original data and the L2 norm is the input (⁠$X$⁠) to our VAE model. This normalization technique is chosen because it ensures the process characteristics are in a consistent scale.

Considering that the VAE model relies on the quality and quantity of the input data, we increased the total size of the input dataset by splitting each process into a minimum and maximum version. This split means that each process is represented twice, using the maximum and minimum values of the process’s range for process time, affected volume, tolerance, and surface quality. By separating each process into two versions, we increased the number of processes in the input dataset from 55 unique processes with 21 features (55, 21) to 110 processes with 21 features (110, 21).

VAE architecture

The VAE model we utilized contains two submodules: an encoder and a decoder, each consisting of three layers. The encoder’s input layer compresses the number of features from 21 to 16, maintains this dimension in the hidden layer, and finally compresses to a set of latent coordinates in the output layer. We selected two dimensions for our hidden features due to their interpretability—in 2D space feature heatmaps. Within this 2D latent space, it is feasible to explore based on several process characteristics. In contrast, a 3D latent space would reduce interpretability and complicate the analysis. From these two latent dimensions, the decoder then inversely follows the encoder’s layer order. The benefit of using a simple architecture with a low number of layers is that it enables fast encoding and decoding times, which is crucial for visualizing large and high-resolution feature maps of each process characteristic in the latent space.

Additionally, this simplicity helps avoid overfitting, which is particularly important given our small dataset of 110 data points, each with 21 features. Increasing the number of hidden layers or features beyond this threshold risks overfitting, where the model would start memorizing the data instead of generalizing effectively. This tradeoff between model complexity and dataset size was crucial for ensuring a robust and generalized model, enabling us to explore the inclusion of new process characteristics and maintain consistency across expanding datasets. Furthermore, this expansion of the dataset is computationally inexpensive due to the small dataset size and the efficiency of the current architecture, with training wall times typically within 1–2 min. This ensures that re-training the model is not a concern when additional characteristics are included, as this architecture supports efficient exploration of the latent space, facilitating the discovery of new processes even with a relatively small dataset.

While our current VAE model does not directly produce confidence intervals, methods like Bayesian inference or Monte Carlo Dropout could be employed to provide explicit uncertainty quantification (51). These techniques would enable us to generate process characteristics along with associated confidence bounds. However, given the small architecture of our model (1,369 trainable parameters), we anticipate that the prediction uncertainty will not significantly impact the conclusions drawn in the “Results” section. Any prediction uncertainty is realized as variations in process characteristics within the latent space, particularly in regions with sparse data (data-void regions) (52). Since our analysis primarily focuses on regions near the origin, where the training data are concentrated, we expect minimal uncertainty in these areas.

The reconstruction accuracy and correlations between process characteristics improve when using the Gaussian Error Linear Unit (GELU) as the activation function for the decoder’s output layer. GELU is a Gaussian cumulative distribution function following the standard normal distribution (N(0,1)), using the approximation:

where x is our input data (53). Given that the VAE’s encoder represents the input dataset with a Gaussian distribution, employing GELU provides a smooth transition between feature boundaries in the latent space. While traditional activation functions like ReLU (⁠$max(0,x)$⁠) lead to nonnegative outputs, allowing negative outputs in this work improves reconstruction accuracy. To enable small negative outputs during the VAE’s learning, we use the LeakyReLU (⁠$max(0.01x,x)$⁠) activation function in the encoder’s hidden layers.

VAE learning procedure

Minimizing the KL loss, which governs the generative capabilities of the VAE model, reduces the deviation between the true dataset distribution and the encoder’s Gaussian distribution. As the KL loss decreases, the reconstruction loss tends to increase. Rather than equally minimizing both losses, researchers have found that introducing a cyclic anneal schedule on the weight of the KL loss can further minimize the reconstruction error (54). Cyclic annealing involves linearly increasing the weight (β) of the KL loss’s penalty term, shown in Eq. 1, from 0 to 1 over a scheduled number of iterations. The main purpose of this procedure is to overcome KL vanishing, which occurs when the penalty term is kept constant (⁠$β=1$⁠). In our case, when utilizing the full penalty term, the KL loss minimizes close to zero and remains constant, causing the reconstruction loss to increase and resulting in poor reconstruction accuracy. The impact of minimizing the KL loss on reconstruction accuracy stems from the Gaussian assumption made by the VAE regarding the input’s distribution.

In this study, we found that a scheduled increase in the penalty term leads to a significantly high reconstruction loss. To address this issue, we developed a scheduling scheme, illustrated in Fig. 6 that utilizes a minimal but impactful amount of the penalty term. The VAE learning procedure begins by developing the model without the KL loss term (⁠$β=0$⁠), effectively turning the VAE into a traditional AE and prioritizing initial reconstruction accuracy. After the first 250 iterations, the KL loss increases from 0.5 to 10.0. In the next 250 iterations, we minimize the KL loss with a penalty term of 0.005, activating when the KL loss exceeds 1.0. Finally, in the third step, we diminish the penalty term using the ratio $β=0.01$/iteration, where iteration ranges from 0 to 500. This step results in an increase in the KL loss from 0.56 to 4.2. By implementing this schedule for the penalty term, we obtain the VAE’s loss function (ELBO) shown in Fig. 6. The visible spikes seen in Fig. 6 are due to the use of the KL divergence term during training, which enforces a generalized latent space representation by regularizing the model’s learned distribution to approximate a standard Gaussian. This regularization prevents overfitting by discouraging the model from memorizing to the individual data points.

Even though our learning procedure utilized a small percentage of the penalty term, the overall process distribution in the latent space closely follows a Gaussian shape, as depicted in Fig. 3. This Gaussian distribution is indicative of the effect of the KL loss term in the model, which encourages the latent variables to conform to a standard normal distribution. The VAE model was implemented on a CPU using the PyTorch package (55).

Acknowledgments

The authors would like to thank Sanjana Subramaniam and Tuba Dolar for proofreading and providing feedback during manuscript preparation.

Funding

This work was funded by the Department of Defense Vannevar Bush Faculty Fellowship, USA N00014-19-1-2642.

Author Contributions

D.Q. contributed to conceptualization, formal analysis, investigation, methodology, visualization, and manuscript writing. D.K. contributed to conceptualization, formal analysis, and manuscript review and editing. M.M. contributed to conceptualization, funding acquisition, investigation, and manuscript review and editing. T.X. contributed to conceptualization, investigation, and manuscript review and editing. J.C. contributed to conceptualization, funding acquisition, methodology, project administration, supervision, and manuscript review and editing.

Data Availability

The manufacturing database and code have been deposited in GitHub at https://github.com/dqs2771/MFG-VAE.

References

Author notes